Meissels mathematical interests covered the following fields number theory in particular properties of prime numbers  theta functions elliptic functions spherical trigonometry hydrodynamics ordinary differential equations asymptotic expansions and Bessel functions

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Meissel's mathematical interests covered the following fields: number theory (in particular, properties of prime numbers ), theta functions, elliptic functions, spherical trigonometry, hydrodynamics, ordinary differential equations, asymptotic expansions, and Bessel functions.